Studies of Exactly Solvable Models in Statistical Mechanics

0100041Perk和Au-Yang这是一个研究统计力学的精确可解模型的研究项目，包括可积手征Potts模型和各种伊辛模型。这些模型将通过精确的解析和近似的数值方法进行研究。将研究各种物理现象，如准周期或非周期晶格中的临界现象、公度-非公度相变和挫折。我们将通过研究部分和完全受挫的三角形或棋盘状伊辛模型来分析受挫对波矢相关磁化率的影响。对于复杂性呈多项式增长的平面伊辛模型的磁化率级数，将开发新的算法，并将分析由此产生的长级数展开，以更好地理解对标度的修正。在可积的手征Potts模型中，许多具有挑战性的问题仍有待解决，如磁化强度、自旋-自旋和能量-能量关联。就其本质而言，这个项目还涉及到当前感兴趣的几个数学领域。

0100041Perk and Au-YangThis is a research project for the study of exactly solvable models of statistical mechanics, including the integrable chiral Potts model and various Ising models. These models will be studied by exact analytical and approximate numerical methods. Various physical phenomena will be studied, such as critical phenomena in quasi-periodic or aperiodic lattices, commensurate-incommensurate phase transitions, and frustration. The impact of frustration on the wavevector-dependent susceptibility will be analyzed by studying partially and fully frustrated triangular or checkerboard Ising models. New algorithms for the susceptibility series of planar Ising models, whose complexity grow polynomially, will be developed and the resulting long series expansions will be analyzed to get a better understanding of corrections to scaling. Many challenging problems remaining to be solved within the integrable chiral Potts model, such as the magnetization, spin-spin and energy-energy correlations. By its very nature, this project also involves several areas of mathematics of current interest.